Court spokesman Kim Mun-sung said the court's ruling was to take effect immediately, although companies often request that sanctions be suspended while they evaluate their legal options.
Nam Ki-yung, a spokesman for Samsung, said the company welcomed the ruling.
"Today's ruling also affirmed our position that one single company cannot monopolize generic design features," he said.
Apple did not respond to multiple calls seeking comment.
The court also ordered each company to pay monetary compensation to its competitor. Samsung must pay Apple 25 million won ($22,000) while Apple must pay its rival 40 million won.
South Korea is not a big market for Apple, and the ruling is not likely to have a big impact on jury deliberations in the U.S.
However, some industry watchers expressed concern over the South Korean ruling to protect industry standard patents. They say the decision could invite a trade war by giving Samsung and fellow South Korean company LG -- both industry standard patent holders -- more room to block rivals' entrance into South Korea if they don't agree to licensing terms.
"It would mean that foreign companies would either have to bow to Samsung's and LG's demands ... or stop selling in Korea," said Florian Mueller, a patent expert in Munich, Germany who has been closely following the case.
Courts in Europe, including Netherlands, France, Italy and Germany have rejected similar claims by Samsung that Apple violated its wireless patents, with judges arguing that the patents have become part of industry standards. Standard-essential patents are a crucial technology for new players to make products compatible with the rest of the market and must be licensed under fair and reasonable terms.
Europe's anti-trust regulator launched an investigation earlier this year into whether Samsung was failing to license those patents under fair and reasonable terms.